MOC-Z Models for Transient Gaseous Cavitation in Pipe Flow

Abstract

The paper presents models based on the method of characteristics (MOC) for transient gaseous cavitation in pipe flow. Two predictor-corrector steps are considered, in which only the term pertaining to the gas fraction is computed along the longitudinal direction, whereas all the other terms are calculated along the characteristic lines (MOC-Z). These models, both one-dimensional (1D) and two-dimensional (2D), were presented previously and analyzed for transient vaporous cavitation in pipe flow; this study extended the models to transient gaseous cavitation, with a proper and different expression of an auxiliary variable. The empirical parameters of the gaseous cavitation models were calibrated by a micro-genetic-algorithm. The results of the proposed numerical method were compared both with experimental values and with those obtained by the MacCormack scheme. When a gas release model was considered in addition, with a proper balance equation, the proposed numerical methods performed best: in such cases, the results almost overlap those of the MacCormack scheme, but the MOC does not need to search for the proper Courant number for stability. The proposed method is much simpler and straightforward than the classic MOC, basically because no interpolation must be used.